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  1. #1
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    positive definite



    Hi there,

    I have a short algebra question.

    I have matrix A1, and A2.

    Both matrices are 2 by 2. Both matrices have all elements positive. Both matrices are symmetric. Matrix A1 has all elements greater than the CORRESPONDING ones of A2.

    i.e. A1(11)>A2(11), A1(12)>A2(12), A1(21)>A2(21), A1(22)>A2(22).


    I would like the following to be true (I don't know if it is)

    A=A1-A2 is nonegative definite.


    It is a bit hard to get the det(A) and see if it is positive. Is there any property that could help me?


    Thanx in advance.

  2. #2
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    The only way I know is the evaluate the determinant. Why is that so hard ?

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